In this case, fundamental attribution error is about placing blame on a cause that you can't prove. Seeking the cause of something in others is a way to make sense of the world. BBC explains:

When we observe other people we attribute their behaviour to their character rather than to their situation—my wife's carelessness means she loses her keys, your clumsiness means you trip over, his political opinions mean that he got into an argument.

When we think about things that happen to us the opposite holds. We downplay our own dispositions and emphasise the role of the situation. Bad luck leads to lost keys, a hidden bump causes trips, or a late train results in an unsuccessful job interview—it's never anything to do with us.

Unfortunately, the only real solution is to recognize that your brain works this way. BBC suggests recognizing the behavior might be enough:

In more prosaic domestic moments, when it feels like such bad luck that I can't find my keys, yet my wife seems so careless when she can't find hers, I know I'm performing psychological magic. I'm observing the myriad events in the world and imagining things—my bad luck, her carelessness—which I use to explain the world with.

[T]he next time you find yourself being cut off from your lane as you are driving (or something similar happens), notice the nature of your spontaneous interpretations: are they negative or positive? That will give you a clue as to whether you have scope to become less cynical.

So, the next time you think of someone as careless, keep in mind what the real root cause of that statement might be. You might be surprised at the assumptions you're making.